Math 1050-003 Final Exam Practice Test December 2, 2013

Note that this Practice Test is longer than the Final Exam will be.This way you have extra problems to help you practice, so don’t let thelength scare you.Try not to use your notes while you work on these problems.NO CALCULATORS

You might find the following formulas helpful. The same formulas will be given to you onthe actual exam. Make sure you know how to use them!

ax2 + bx+ c = a(x+b

2a)2 + c− b2

4a

α1,2 =−b±

√b2 − 4ac

2a

an = a1 + d(n− 1)

n∑i=1

ai = n(a1 + an)/2

an = a1 ∗ rn−1

∞∑i=1

ai =1

1− r

Math 1050-003 Final Exam Practice Test Page 2 of 41.

MULTIPLE CHOICE ANSWERS

1.

2.

Cont.

Math 1050-003 Final Exam Practice Test Page 3 of 41

3. Suppose f(x) is the piecewise dened function given below. Graph f(x).

f(x) =

{x+ 1 if x ∈ (−∞,−2)

x+ 3 if x ∈ [−2,∞)

4. Suppose f(x) is the piecewise dened function given below. Graph f(x).

f(x) =

{x2 if x 6= 5

−1 if x = 5

Cont.

Math 1050-003 Final Exam Practice Test Page 4 of 41

5. Suppose f(x) is the piecewise dened function given below. Graph f(x).

f(x) =

{x3 if x ∈ (−∞, 1)

−2 if x ∈ [1,∞)

6. Suppose f(x) is the piecewise dened function given below. Graph f(x).

f(x) =

{3x if x 6= 2

x2 if x = 2

Cont.

Math 1050-003 Final Exam Practice Test Page 5 of 41

7. Whats the slope of the line 30x− 6y = 3?

Answer:

8. Whats the slope of the line −10x+ 5y = 4?

Answer:

9. Whats the slope of the line 6x+ 3y = 237?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 6 of 41

Each of the systems below has a unique solution. Find the solution.

10. {8x+ 4y = 12

x− 7y = −21

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 7 of 41

11. {10x− 3y = 52

−3x+ y = −16

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 8 of 41

12. {3x = 5

2x− 3y = 12

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 9 of 41

13. {2x+ 8y = −8

−3x+ 6y = 12

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 10 of 41

14. Find

(32

)+

(47

)

Answer:

15. Find

(92

)+

(131

)

Answer:

16. Find 3

(45

)

Answer:

17. Find 11

(32

)

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 11 of 41

18. Find the product

(3 52 6

)(1 43 2

)

Answer:

19. Find the product

(2 15 6

)(3 71 3

)

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 12 of 41

20. Find the product

2 1 00 0 61 3 0

0 0 23 0 10 0 5

Answer:

21. Find the product

0 0 23 0 10 0 5

2 1 00 0 61 3 0

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 13 of 41

22. Find the determinant

det

(2 15 6

)

Answer:

23. Find the determinant

det

(3 75 2

)

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 14 of 41

24. What is the inverse of

(3 15 2

)?

Answer:

25. What is the inverse of

(1 12 5

)?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 15 of 41

26. Use that 4 3 33 1 2−1 −1 −1

−1 =

1 0 31 −1 1−2 1 −5

to find a solution for

4x+ 3y + 3z = 2

3x+ y + 2z = 4

−x− y − z = 22

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 16 of 41

27. Use that 3 −1 −18 10 32 3 1

−1 =

1 −2 7−2 5 −174 −11 38

to find a solution for

3x− y − z = 1

8x+ 10y + 3z = 7

2x+ 3y + z = 4

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 17 of 41

1. (2 pt) Which of the following is a true statement?

(a) Z ⊆ R ⊆ Q ⊆ N(b) N ⊆ Z ⊆ Q ⊆ R(c) Z ⊆ N ⊆ Q ⊆ R(d) N ⊆ Q ⊆ R ⊆ Z

2. (2 pt) {x,@, ∗} ⊆ {x, !, ∗,@,+}

(a) True

(b) False

3. (2 pt) {x,@, ∗} ⊆ {x, !,@,+}

(a) True

(b) False

Cont.

Math 1050-003 Final Exam Practice Test Page 18 of 41

4. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither.

2, 5,−10, 8, ...

(a) arithmetic

(b) geometric

(c) neither

5. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither.

−2,−4,−8,−32, ...

(a) arithmetic

(b) geometric

(c) neither

6. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither.

3, 7, 24, 31, ...

(a) arithmetic

(b) geometric

(c) neither

7. (2pt) Decide whether the given sequence is arithmetic, geometric, or neither.

6, 36, 66, 96, ...

(a) arithmetic

(b) geometric

(c) neither

Cont.

Math 1050-003 Final Exam Practice Test Page 19 of 41

8. (4pt) Find100∑i=1

5

(a) 5

(b) 500

(c) 100

(d) 250

9. (4pt) Find40∑i=1

i

(a) 40

(b) 1

(c) 1640

(d) 820

Cont.

Math 1050-003 Final Exam Practice Test Page 20 of 41

10. (4pt) What is the sum of the first 41 terms of the sequence 0, 2, 4, 6, ...?

(a) 1640

(b) 2

(c) 80

(d) 3280

11. (4pt) What does the following series equal: 2 +2

3+

2

9+

2

27+ ...?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 21 of 41

12. (4 pt) You have three pairs of shoes, five pairs of pants, six shirts, two jackets, andthree hats to choose from. How many different outts can you put together that useone pair of shoes, one pair of pants, one shirt, one jacket, and one hat? Your answershould be a real number.

Answer:

13. (4 pt) There are 9 people on a boat. One person needs to be the captain, one needsto be the first mate, and you need a person to swab the decks (no person can do morethan one job). How many different ways can those three jobs be filled by the 9 peopleon board? Your answer should be a real number.

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 22 of 41

14. (4 pt) A sports team is selling season ticket plans. They have 15 home games ina season, and they allow people to purchase tickets for any combination of 9 homegames. How many ways are there to choose a collection of 9 home games? Youranswer may have factorials in it.

Answer:

15. (4 pt) What is

(50

3

)? Simplify your answer all the way.

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 23 of 41

16. (2 pt) Draw the first 10 rows of Pascal’s Triangle.

17. (4 pt) Use the Binomial Theorem and Pascal’s Triangle above to expand (x − 1)8.Simplify each term as much as possible.

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 24 of 41

18. (1pt Extra Credit) What does the following series equal: 2 + 6 + 18 + 54 + ...?

Answer:

19. (2 pts) (True/False) 7x5 + 13x4 − 3x3 − 7x2 + 2x− 1 has 8 roots.

Answer:

20. (2 pts) (True/False) 3x− 5 has 1 root.

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 25 of 41

21. (2 pts) What is the slope of p(x) = 13x+ 2?

Answer:

22. (2 pts) What is the slope of p(x) = πx+ 97?

Answer:

23. (3 pts) Graph p(x) = 3x− 2

24. (3 pts) Graph p(x) = −2x+ 3

Cont.

Math 1050-003 Final Exam Practice Test Page 26 of 41

Cont.

Math 1050-003 Final Exam Practice Test Page 27 of 41

25. (2 pts) What is the y intercept of p(x) = 5x+ 1000?

Answer:

26. (2 pts) What is the x intercept of p(x) = 5x+ 1000?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 28 of 41

For the next 7 questions consider p(x) = 5x2 − 15x+ 10

27. (3 pts) Complete the square

Answer:

28. (3 pts) What’s the vertex of the corresponding parabola?

Answer:

29. (2 pts) Is the parabola opening up or down?

Answer:

30. (3 pts) What’s its discriminant?

Answer:

31. (2 pts) How many roots does it have?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 29 of 41

32. (4 pts) What are its roots?

Answer:

33. (5 pts) Use the previous 6 questions to graph p(x) labeling its vertex and any x and yintercepts.

Cont.

Math 1050-003 Final Exam Practice Test Page 30 of 41

For the next 7 questions consider p(x) = −4x2 − x+ 5

34. (3 pts) Complete the square

Answer:

35. (3 pts) What’s the vertex of the corresponding parabola?

Answer:

36. (2 pts) Is the parabola opening up or down?

Answer:

37. (3 pts) What’s its discriminant?

Answer:

38. (2 pts) How many roots does it have?

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 31 of 41

39. (4 pts) What are its roots?

Answer:

40. (5 pts) Use the previous 6 to graph p(x) labeling its vertex and any x and y intercepts.

Cont.

Math 1050-003 Final Exam Practice Test Page 32 of 41

41. (8 pts) Fully factor 4x3 − 20x2 + 25x− 3

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 33 of 41

42. (8 pts) Fully factor 5x3 − 9x2 + 8x− 20

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 34 of 41

43. (4 pts) Graph −(x− 1)(x− 2)(x− 2)(x− 3)(x2 + x + 5) making sure to show all thex intercepts and behavior on the far right and left.

Cont.

Math 1050-003 Final Exam Practice Test Page 35 of 41

44. (4 pts) Graph 13x(x + 1)(x− 2)(x + 2)(x− 3)(2x2 + 3x + 3) making sure to show allthe x intercepts and behavior on the far right and left.

Cont.

Math 1050-003 Final Exam Practice Test Page 36 of 41

45. (3 pts) If a is a real nuimber, a0 =

(a) 0

(b) 1

(c) a

(d) ∞

46. (3 pts) If a is a real nuimber, a1 =

(a) 0

(b) 1

(c) a

(d) ∞

47. (3 pts) 4−32

(a) 4

(b) 8

(c) −8

(d) 18

(e) −18

(f) −12

(g) Not Defined

Cont.

Math 1050-003 Final Exam Practice Test Page 37 of 41

48. (3 pts) If 8x =1

4, then x =

(a) 2

(b) −2

(c)1

2

(d) −1

2

(e) −3

2

(f) −2

3

(g)3

2

(h)2

3(i) Not Defined

49. (3 pts) If a is a real nuimber,loga(1) =

(a) 0

(b) 1

(c) a

(d) ∞(e) Not Defined

50. (3 pts)log2(4) =

(a) 0

(b) 1

(c) 2

(d) 12

(e) 16

Cont.

Math 1050-003 Final Exam Practice Test Page 38 of 41

51. (3 pts)

log5(1

25) =

(a) 0

(b) 1

(c) 2

(d)1

2(e) −2

(f) ∞

52. (5 pts) Solve for x:53x−2 = 125

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 39 of 41

53. (5 pts) Solve for x:log2(x)− log2(x+ 4) = 3

Answer:

54. (5 pts) Solve for x:log3(15x) + log3(x+ 1) = 4

Answer:

Cont.

Math 1050-003 Final Exam Practice Test Page 40 of 41

55. (10 pts) Graph f(x), making sure to show VERTICAL ASYMPTOTES, X INTER-CEPTS, and BEHAVIOR AT FAR RIGHT AND FAR LEFT.

f(x) =2(x− 3)(x+ 1)

x(x+ 3)

Cont.

Math 1050-003 Final Exam Practice Test Page 41 of 41

56. (10 pts) Graph f(x), making sure to show VERTICAL ASYMPTOTES, X INTER-CEPTS, and BEHAVIOR AT FAR RIGHT AND FAR LEFT.

f(x) =−5(x− 3)(x+ 1)(x− 2)

x(x+ 3)(x2 − 5x)

The End.